Stable process with singular drift

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On weak uniqueness and distributional properties of a solution to an SDE with α-stable noise (2015, result): “4] for other related topics: the heuristics for the choice of the zero-order term in the parametrix expansion, the related papers which concern SDEs with singular drift terms ([Po94], [PP95], [BJ07], [KS14]), the related results of [KS14] and [CW13] on weak uniqueness for gradient perturbations of s”
Parametrix construction of the transition probability density of the solution to an SDE driven by $\alpha$-stable noise (2014, background): “In [35] this result is extended even further, with b being allowed to be a generalized function equal to the derivative of a measure from Kd,α−1.”
Uniqueness of stable processes with drift (2013, background): “However, the existence and uniqueness of the solution in [7] is formulated in a weaker sense, as in [2].”